## Triangle – Area problem

In triangle * ABC*, cevians

**,**

*AD***and**

*BE***intersect at point**

*CF***. The areas of triangles**

*P***,**

*PAF***,**

*PFB***and**

*PBD***are**

*PCE***,**

*40***,**

*30***and**

*35***, respectively. Find the area of triangle**

*84***.**

*ABC***TIPS:**Let the area of triangle **PEA** be * x* and area of triangle

**be**

*PCD**. Now use the proportion of areas of triangles.*

**y**Now use system of linear equations and find ** x** and

**. The area of triangle**

*y**is*

**ABC****.**

*189+x+y*

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Categories: Triangles
area, geometry, proportion, system equation, triangle

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